Computing Monetary Risk Measures in Linear Time
This work provides faster computation of widely used monetary risk measures, benefiting practitioners in finance and risk management who need to process large datasets.
The authors propose new algorithms, QuickVaR and QuickDivergence, that compute Value-at-Risk and Conditional-Value-at-Risk for discrete random variables in expected linear time, achieving an order-of-magnitude speedup for large domains.
Monetary risk measures have gained popularity for expressing decision-makers' risk aversion. Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR), in particular, are used commonly for this purpose. This paper proposes new efficient algorithms to compute these risk measures for a discrete random variable in expected linear time with respect to the size of its domain. First, we propose a QuickVaR algorithm that computes the VaR of a discrete random variable. Then, we leverage QuickVaR to propose QuickDivergence, an algorithm for computing a class of $φ$-divergence risk measures, including the popular CVaR risk measure. The QuickVaR algorithm adapts the well-known Quickselect algorithm, while QuickDivergence builds on polymatroid optimization algorithms. Numerical results show that our new algorithms offer an order-of-magnitude speedup for large domains, and a library implementation of the algorithms is available at https://github.com/RiskAverseRL/RiskMeasures.jl.